As the question says, what should we infer is happening when it's reported that the bond market is surging or rallying?
Is the implication that bond prices are increasing? Or is that yields are increasing, if so, which measure of bond yield?
The price is going up. The bond you own can now be sold for more.
This means that the effective interest rate for someone buying it at this new higher price is falling and suggests that buyers are willing to accept a lower interest rate now than you were when you bought it.